Overall, model experiments show a CO2 equilibration time of a few centuries [5, 6, 11, 12]. (realclimate.org)
However, the ocean mixed layer equilibrates quickly to the atmospheric concentration, but has a very slow equilibration time with the deep ocean. (realclimate.org)
So on the time scale for temperature equilibration of the Earth, you'd probably have less than a doubling of atmospheric CO2, not enough to get 5 degrees C if the climate sensitivity is as today about 3 degrees C. (realclimate.org)